Question

A student moves a box of books down the hall
by pulling on a rope attached to the box. The
student pulls with a force of 173 N at an angle
of 26.7
◦
above the horizontal. The box has a
mass of 42.4 kg, and µk between the box and
the floor is 0.2.
The acceleration of gravity is 9.81 m/s
2
.
Find the acceleration of the box.
Answer in units of m/s
2
.

Answer 1

From the equation,

$F=ma\newline F-F'=ma\newline$

where F=force parallel to the floor

F′=Frictional force

m=mass of the box

a=acceleration

$\newline 173cos(26.7)-F'=42.4a \to(1)$

Considering the forces perpendicular to the floor

$mg=R+173sin26.7 \\~\\$

solving this gives

$R=338.2N \newline$

From, F′=μRF

$F'=67.64N \newline$

Substituting to (1)

$\underline{\underline{{a=2.05ms^{-2}}}}$